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Finite element simulation of a saltwater/freshwater interface with indirect toe tracking
Author(s) -
Wilson John L.,
Sa Da Costa Antonio
Publication year - 1982
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr018i004p01069
Subject(s) - grid , finite element method , nonlinear system , gaussian quadrature , aquifer , quadrature (astronomy) , geology , boundary value problem , saturation (graph theory) , mechanics , geotechnical engineering , mathematical analysis , mathematics , geometry , groundwater , engineering , structural engineering , physics , nyström method , electrical engineering , quantum mechanics , combinatorics
The porous media two‐layer flow problem involving fluids of different density separated by an immiscible interface is solved using the Galerkin finite element method in one dimension. Each layer is present only over a portion of the domain. The transition from two layers to one constitutes a moving boundary which must be calculated as part of the solution. An indirect numerical procedure using a fixed grid is proposed to track the boundary. The procedure uses the Gaussian quadrature points, a nonlinear variation of layer saturation across those elements containing a moving boundary and an imaginary ‘extra thickness’ of the absent layer. It is illustrated with an application to the gravity segregation problem. In this example the model performs as accurately as and is considerably less expensive than equivalent grid regeneration or moving grid schemes. The primary area of application is to the prediction of sea water intrusion in groundwater aquifers using regional, essentially horizontal flow models.